Paul Krugman suggests that District 11 and District 12 don't appear to have enough exploited people to support the large and propserous Capitol.
We can look at this quite precisely in the case of District 12, which based on the text is the only source of coal in all of Panem and has a population of just 8,000 people not all of whom are coal miners. By contrast, present-day West Virginia contains 21 separate municipalities with a population that large or larger, with Huntington and Charleston each containing 50,000 inhabitants. I considered delving into this in my article on the Economics of the Hunger Games, but the obvious interpretation is that the productivity in the Panem mining sector is just off the charts compared with what we have today. And why shouldn't it be? We see that Panem is an extremely technologically advanced society relative to our own in a number of respects. We don't see Panem's coal-mining technology displayed in any kind of detail—don't let the old-timey outfits the miners wear fool you; they're using something incredibly advanced down there that's on a par with the advanced technology we see used in the creation and manipulation of the Arena. In a democratic society we might expect such high productivity mines to be associated with high wages for miners, but Panem's exploitative political institutions lead to extractive economic institutions and thus the riches of District 12's mines no more trickle down to the workers than did the wealth of the Spanish Empire's gold mines trickle down to the enslaved indigenous workforce. The small size of the District 12 population is crucial to understanding the full extent of the exploitation that's happening.
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